这本质上是一种称为“最小集合覆盖问题”的优化问题。

from typing import List, Dict, Set

def min_set_cover(photos: Dict[str, Set[str]]) -> List[str]:
    # Sort photos by the number of people, in descending order
    photos = sorted(photos.items(), key=lambda x: len(x[1]), reverse=True)

    result = []
    photographed = set()

    while photos:
        # Select the group with the maximum intersection with photographed people and minimum new people
        next_photo = max(photos, key=lambda x: (len(x[1] & photographed), -len(x[1])))
        result.append(next_photo[0])
        photographed |= next_photo[1]
        photos.remove(next_photo)

    return result

photos = {
    'photo1': {'Bride', 'Groom', 'Mom1', 'Dad1'},
    'photo2': {'Bride', 'Mom1', 'Dad1'},
    'photo3': {'Groom', 'Mom1', 'Dad1'},
    'photo4': {'Bride', 'Groom', 'Mom2', 'Dad2'}
}

print(min_set_cover(photos))  # Output: ['photo1', 'photo4', 'photo3']